基于分形理论的粗粒土缩尺效应及强度性质研究

Study on Mechanics Characteristics of Coarse Grained Soil with Different Gradation Based on Fractal Theory

基于分形理论研究了同种材料不同缩尺方法和不同缩尺粒径对分形维数的影响,并通过常规三轴剪切试验建立了分形维数与抗剪强度指标的相互关系。结果表明,与原型级配的粒度分形曲线相比,不同缩尺法得到的粒度分形曲线形态有较大差异,缩尺级配的分形维数均小于原型级配的分形维数,分形维数在数值上能表征土的级配;不同缩尺法得到的峰值强度变化规律与分形维数变化规律一致,在高围压下分形维数越大,不同缩尺法之间的峰值强度差也越大;凝聚力c随着分形维数的减小而增大,而内摩擦角φ随着分形维数的增大而增大,两者近似一抛物线关系,并根据拟合表达式推导出了原型级配的φ值,具有一定的工程指导意义。

The influences of scale methods and particle sizes for fractal dimension were analyzed based on fractal ge ometry theory. The relationship between fractal dimension and shear strength index was also established through conven tional triaxial shear test. The results show that compared to fractal dimension curve of prototype gradation, fractal di mension curves of different scale methods have great differences, fractal dimensions of different scale methods are all smaller than prototype gradation^s, and fractal dimension can numerically express the soil gradation; peak strength and fractal dimension have the same change rule for different scale methods; and in high confining pressure, the bigger of fractal dimension is, the larger of peak stress difference is; meanwhile, the value of cohesion c increases with the decrea- sing of fractal dimension, but opposite the value of friction angle φ parabolic relationships have been found between φ and fractal dimension, and the φ of prototype gradation can also be deduced from that expression, which has significance for an actual engineering.